%I A046899
%S A046899 1,1,2,1,3,6,1,4,10,20,1,5,15,35,70,1,6,21,56,126,252,1,7,28,84,210,
%T A046899 462,924,1,8,36,120,330,792,1716,3432,1,9,45,165,495,1287,3003,6435,
%U A046899 12870,1,10,55,220,715,2002,5005,11440,24310,48620,1,11,66,286,1001
%N A046899 Triangle in which n-th row is {C(n+k,k), k=0..n}, n >= 0.
%C A046899 Row sums = A134391: (1, 3, 10, 35, 126, 362, 1726,...). - Gary W. Adamson 
               (qntmpkt(AT)yahoo.com), Oct 23 2007
%C A046899 T(n, k) is also the number of order-preserving full transformations (of 
               an n- chain) of waist k (waist(alpha) = max(Im(alpha))). [From A. 
               Umar (aumarh(AT)squ.edu.om), Oct 02 2008]
%D A046899 H. W. Gould, A class of binomial sums and a series transformation, Utilitas 
               Math., 45 (1994), 71-83.
%D A046899 Laradji, A. and Umar, A. Combinatorial results for semigroups of order-preserving 
               partial transformations. Journal of Algebra 278 (2004), 342-359. 
               [From A. Umar (aumarh(AT)squ.edu.om), Oct 02 2008]
%D A046899 Laradji, A. and Umar, A. Combinatorial results for semigroups of order-preserving 
               full transformations. Semigroup Forum 72 (2006), 51-62. [From A. 
               Umar (aumarh(AT)squ.edu.om), Oct 02 2008]
%e A046899 1
%e A046899 1, 2
%e A046899 1, 3, 6
%e A046899 1, 4, 10, 20
%e A046899 1, 5, 15, 35, 70
%e A046899 1, 6, 21, 56, 126, 252
%e A046899 1, 7, 28, 84, 210, 462, 924
%e A046899 1, 8, 36, 120, 330, 792, 1716, 3432
%e A046899 1, 9, 45, 165, 495, 1287, 3003, 6435, 12870
%e A046899 1, 10, 55, 220, 715, 2002, 5005, 11440, 24310, 48620
%e A046899 1, 11, 66, 286, 1001, 3003, 8008, 19448, 43758, 92378, 184756
%p A046899 for n from 0 to 10 do seq( binomial(n+m,n), m = 0 .. n) od; - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Dec 09 2007
%Y A046899 Cf. A046900, A134391.
%Y A046899 Sequence in context: A036038 A078760 A103280 this_sequence A035206 A115196 
               A093346
%Y A046899 Adjacent sequences: A046896 A046897 A046898 this_sequence A046900 A046901 
               A046902
%K A046899 nonn,tabl,easy,nice
%O A046899 0,3
%A A046899 N. J. A. Sloane (njas(AT)research.att.com).
%E A046899 More terms from James A. Sellers (sellersj(AT)math.psu.edu)